ADMM-Based Distributed MPC with Control Barrier Functions for Safe Multi-Robot Quadrupedal Locomotion
Authors: Yicheng Zeng, Ruturaj S. Sambhus, Basit Muhammad Imran, Jeeseop Kim, Vittorio Pastore, Kaveh Akbari Hamed
Organizations: Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA · The University of Texas at El Paso, El Paso, TX 79968, USA
This paper proposes a fully decentralized model predictive control (MPC) framework with control barrier function (CBF) constraints for safety-critical trajectory planning in multi-robot legged systems. The incorporation of CBF constraints introduces explicit inter-agent coupling, which prevents direct decomposition of the resulting optimal control problems. To address this challenge, we reformulate the centralized safety-critical MPC problem using a structured distributed optimization framework based on the alternating direction method of multipliers (ADMM). By introducing a novel node-edge splitting formulation with consensus constraints, the proposed approach decomposes the global problem into independent node-local and edge-local quadratic programs that can be solved in parallel using only neighbor-to-neighbor communication. This enables fully decentralized trajectory optimization with symmetric computational load across agents while preserving safety and dynamic feasibility. The proposed framework is integrated into a hierarchical locomotion control architecture for quadrupedal robots, combining high-level distributed trajectory planning, mid-level nonlinear MPC enforcing single rigid body dynamics, and low-level whole-body control enforcing full-order robot dynamics. The effectiveness of the proposed approach is demonstrated through hardware experiments on two Unitree Go2 quadrupedal robots and numerical simulations involving up to four robots navigating uncertain environments with rough terrain and external disturbances. The results show that the proposed distributed formulation achieves performance comparable to centralized MPC while reducing the average per-cycle planning time by up to 51% in the four-agent case, enabling efficient real-time decentralized implementation.
Figures & tables
Fig. 1: Snapshot of the hardware experiment demonstrating the proposed ADMM-based CBF-DMPC framework, where two Unitree Go2 robots navigate a cluttered environment with rough terrain while maintaining safety-critical inter-agent and obstacle avoidance constraints.
Fig. 2: Overview of the proposed layered control framework, consisting of a high-level ADMM-based CBF-DMPC for safety-critical trajectory planning, a mid-level NMPC layer enforcing the single rigid body (SRB) dynamics, and a low-level whole-body controller (WBC) enforcing full-order robot dynamics.
Fig. 3: Hardware experiments of the proposed ADMM-based CBF-DMPC and layered control with two Unitree Go2 robots: (a) navigation among eight static obstacles (experiment 1), (b) disturbance rejection under external pushes (experiment 2), and (c) obstacle avoidance over rough terrain with ten obstacles (experiment 3). (d) Multi-agent simulation in RaiSim with four robots navigating among ten obstacles.
QP Type
Two Agents
Four Agents
Avg
Std
Avg
Std
Node-update QP
0.51
0.71
0.92
8.34
Edge-update QP
0.002
0.000
0.009
0.003
Total (ADMM)
8.06
10.66
14.58
11.95
Total (Centralized)
9.61
3.87
29.94
21.75
TABLE I: Statistics of QP computation times (ms).
Fig. 4: Plot of the optimal state trajectory (x⋆,i,y⋆,i,θ⋆,i) generated by the high-level ADMM-based CBF-DMPC for agent 1, together with the corresponding reference trajectory toward its goal during experiment 2. The figure also depicts the optimal velocity commands (v⋆,i,ω⋆,i) and the minimum CBF values, representing obstacle-avoidance and inter-agent safety margins. The shaded regions indicate push intervals.
Fig. 5: Comparison between the ADMM-based CBF-DMPC and centralized CBF-MPC for four agents navigating among obstacles in simulation. The resulting xy trajectories demonstrate near-identical motion and safety behavior under both approaches.
This paper presents a safety-critical distributed nonlinear model predictive control (DNMPC) framework for cooperative payload transportation by teams of quadrupedal robots. The proposed approach models the robotic team and the shared payload as a dynamically coupled networked system with rigid holonomic coupling constraints arising from cooperative transportation. To enable distributed real-time optimization, the centralized finite-horizon optimal control problem is decomposed into parallel local NMPC subproblems coordinated through the alternating direction method of multipliers (ADMM). The resulting distributed framework enforces consensus over both payload-state and interaction-wrench trajectories while explicitly incorporating acceleration-level holonomic coupling constraints within the distributed predictive control formulation. Safety-critical obstacle avoidance constraints for both the robotic agents and payload are enforced using higher-order control barrier functions (HOCBFs). The framework is validated through numerical simulations with teams of two, three, and four quadrupedal robots transporting shared payloads in cluttered environments. Real-time experiments on two- and three-robot teams demonstrate safe and robust transportation under payload uncertainty and external disturbances. Compared with centralized NMPC, the proposed framework achieves up to 23% reduction in average NLP solve time while maintaining comparable closed-loop performance. Ablation studies further demonstrate robustness to communication delays and show that explicit payload-state consensus and holonomic constraints substantially improve payload tracking and distributed coordination over existing wrench-only consensus formulations.
Ruturaj S. Sambhus, Kapi Ketan Mehta, Yicheng Zeng +1
Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA
Collaborative transportation of heavy payloads via loco-manipulation is a challenging yet essential capability for legged robots operating in complex, unstructured environments. Centralized planning methods, e.g., holistic trajectory optimization, capture dynamic coupling among robots and payloads but scale poorly with system size, limiting real-time applicability. In contrast, hierarchical and fully decentralized approaches often neglect force and dynamic interactions, leading to conservative behavior. This study proposes an Alternating Direction Method of Multipliers (ADMM)-based distributed model predictive control framework for collaborative loco-manipulation with a team of quadruped robots with manipulators. By exploiting the payload-induced coupling structure, the global optimal control problem is decomposed into parallel individual-robot-level subproblems with consensus constraints. The distributed planner operates in a receding-horizon fashion and achieves fast convergence, requiring only a few ADMM iterations per planning cycle. A wrench-aware whole-body controller executes the planned trajectories, tracking both motion and interaction wrenches. Extensive simulations with up to four robots demonstrate scalability, real-time performance, and robustness to model uncertainty.
Ziyi Zhou, Pengyuan Shu, Ruize Cao +2
The Institute for Robotics and Intelligent Machines, Georgia Institute of Technology.
Multi-robot systems (MRS) are essential for large-scale applications such as disaster response, material transport, and warehouse logistics, yet ensuring robust, safety-aware formation control in cluttered and dynamic environments remains a major challenge. Existing model predictive control (MPC) approaches suffer from limitations in scalability and provable safety, while control barrier functions (CBFs), though principled for safety enforcement, are difficult to handcraft for large-scale nonlinear systems. This paper presents FORMULA, a safe distributed, learning-enhanced predictive control framework that integrates MPC with Control Lyapunov Functions (CLFs) for stability and neural network-based CBFs for decentralized safety, eliminating manual safety constraint design. This scheme maintains formation integrity during obstacle avoidance, resolves deadlocks in dense configurations, and reduces online computational load. Simulation results demonstrate that FORMULA enables scalable, safety-aware, formation-preserving navigation for multi-robot teams in complex environments.
Qintong Xie, Weishu Zhan, Peter Chin
Thayer School of Engineering, Dartmouth College, NH 03784. · Department of Computer Science, The University of Manchester, Manchester M13 9PL, United Kingdom.